Consider the following question and decide which of the statements is sufficient to answer the question.
Question:
Find the value of z,
Statements:
1) `z^2=36+a`
2) a = `x^2 & x=8`. Options are (a) Either 1 or 2 is sufficient (b) Both 1 and 2 are sufficient (c) Only 1 is sufficient (d) Only 2 is sufficient.

Options

A. Either 1 or 2 is sufficient
B. Both 1 and 2 are sufficient
C. Only 1 is sufficient
D. Only 2 is sufficient

Answer

To solve the problem, we need to determine the value of \( z \) based on the provided statements.

### Step-by-Step Solution:

1. **Analyze Statement 1:**
- The first statement given is \( z^2 = 36 + a \).
- Here, \( z \) is dependent on the value of \( a \). Without knowing \( a \), we cannot find \( z \) directly.
- **Conclusion:** Statement 1 alone is not sufficient to determine the value of \( z \).

**Hint:** Check if the equation can be solved without knowing all variables.

2. **Analyze Statement 2:**
- The second statement is \( a = x^2 \) and \( x = 8 \).
- First, we can calculate \( a \):
\[ a = x^2 = 8^2 = 64 \]
- Now we have a specific value for \( a \).

3. **Combine Statements:**
- Now that we have \( a = 64 \), we can substitute this value back into the first statement:
\[ z^2 = 36 + a = 36 + 64 = 100 \]
- To find \( z \), we take the square root of both sides:
\[ z = \sqrt{100} = 10 \quad \text{or} \quad z = -10 \]
- However, since we are interested in the value of \( z \), we can state \( z = 10 \) (considering the principal square root).

4. **Determine Sufficiency:**
- We found that we needed both statements to determine \( z \). Statement 2 provided the value of \( a \), which was necessary for Statement 1 to yield a value for \( z \).

### Final Conclusion:
- Both statements together are necessary to find the value of \( z \).

**Answer:** (b) Both 1 and 2 are sufficient.